Consider the DCHE (REF ) over \(\widetilde{\Omega }_1 \cup \widetilde{\Omega }_2\) .
From the sectorial normalization theorem of Sibuya [1]} and the theorem of Hukuhara-Turrittin[2]} it follows that
the actual fundamental matrix solution \(\Phi _0(x, 0)\)  of the DCHE can be represented as
\(\,\Phi _j(x, 0)=\exp (G x)\,H_j(x)\,\left[x^{\Lambda }\,\exp \left(-\frac{B}{x}\right)\right]_j\,\) 
